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Search: id:A092321
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| A092321 |
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Sum of largest parts (counted with multiplicity) of all partitions of n. |
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+0
12
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| 1, 4, 8, 17, 26, 49, 69, 115, 164, 249, 343, 513, 686, 974, 1314, 1806, 2382, 3232, 4208, 5597, 7244, 9456, 12118, 15687, 19899, 25422, 32079, 40589, 50796, 63805, 79303, 98817, 122179, 151145, 185820, 228598, 279476, 341807, 416051, 506205, 613244
(list; graph; listen)
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OFFSET
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1,2
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FORMULA
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G.f.: Sum(n*x^n/(1-x^n)*Product(1/(1-x^k), k = 1 .. n), n = 1 .. infinity).
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EXAMPLE
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Partitions of 4 are: [1,1,1,1], [1,1,2], [2,2], [1,3], [4]; thus a(4)=4*1+1*2+2*2+1*3+1*4=17.
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MATHEMATICA
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first Needs["DiscreteMath`Combinatorica`"], then f[n_] := Block[{c = 2n, k = 2, p = Partitions[n]}, m = Max @@@ p; l = Length[p]; While[k < l, c = c + m[[k]]*Count[p[[k]], m[[k]]]; k++ ]; If[n == 1, 1, c]]; Table[ f[n], {n, 41}] (from Robert G. Wilson v Feb 18 2004)
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CROSSREFS
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Cf. A006128, A092314, A092322, A092269, A092309, A092313, A092310, A092311, A092268.
Sequence in context: A037242 A158139 A026393 this_sequence A026353 A067773 A008372
Adjacent sequences: A092318 A092319 A092320 this_sequence A092322 A092323 A092324
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KEYWORD
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easy,nonn
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AUTHOR
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Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 16 2004
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(AT)rgwv.com) Feb 18 2004
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